2.6 Decryption Key

Next: 2.7 Inversion Up: 2. Background: Encryption and Previous: 2.5 Encryption Key

2.6 Decryption Key

To produce understandable decrypted text, you need to decrypt the encrypted text. Sometimes we might say decode or decipher instead of decrypt. To decrypt, we undo encryption, i.e. ``run encryption in reverse'' to transform ciphertext into plaintext, as shown Figure 4.

**Figure 4:** Intermediate Decryption Example Using the Caesar Cipher
$\begin{figure} \begin{center}\fbox{\texttt{ \begin{tabular}{*{34}{@{$\,$ }c}l} w... ...& {\rm bottom line: encoded ciphertext} \end{tabular}}}\end{center}\end{figure}$

Observe that Figure 4 has flipped the arrows upside down to show that decryption transforms the bottom line into the top line. Now, compare the character mappings used in Figures 2 and 4:

Figure 2: 'w' $\rightarrow$ 'z', 'e' $\rightarrow$ 'h', the space maps to a space, 'a' $\rightarrow$ 'd', 'p' $\rightarrow$ 's', and so forth.
Figure 4: 'w' $\leftarrow$ 'z', 'e' $\leftarrow$ 'h', the space maps to a space, 'a' $\leftarrow$ 'd', 'p' $\leftarrow$ 's', and so forth.

The mappings in Figure 4 reverse the mappings in Figure 2, which corresponds to the idea of ``running encryption in reverse''. So, to form the decryption key for decoding ciphertext, reverse all the mappings in the encryption key. Figure 5 shows this process for the encryption key from Figure 1.

**Figure 5:** Intermediate Decryption Key for the Caesar Cipher
$\begin{figure} \begin{center}\fbox{\texttt{ \begin{tabular}{*{26}{@{$\,$ }c}l} a... ...bottom line: encoding of each character} \end{tabular}}}\end{center}\end{figure}$

For conciseness and consistency omit arrows but understand that they implicitly point down. So, you must flip Figures 4 and 5 upside down, yielding Figures 6 and 7. Figure 8 summarizes the different types and arrangements of keys.

**Figure 6:** Final Decryption Example Using the Caesar Cipher
$\begin{figure} \begin{center}\fbox{\texttt{ \begin{tabular}{*{34}{@{$\,$ }c}l} z... ... {\rm bottom line: unencoded plaintext} \end{tabular}}}\end{center}\end{figure}$

**Figure 7:** Final Decryption Key for the Caesar Cipher
$\begin{figure} \begin{center}\fbox{\texttt{ \begin{tabular}{*{26}{@{$\,$ }c}l} d... ...t&u&v&w&x&y&z& {\rm top line: alphabet} \end{tabular}}}\end{center}\end{figure}$

**Figure 8:** Summary of Keys
$\begin{figure} \begin{tabular}{c\vert c\vert c\vert c\vert} \multicolumn{1}{c}{}... ...& encoded alphabet & unencoded alphabet \\ \cline{2-4} \end{tabular}\end{figure}$

Next: 2.7 Inversion Up: 2. Background: Encryption and Previous: 2.5 Encryption Key

Thomas Yan
2000-05-01